And checking out if we have 4t instead of 2t...
We have 4t=A(t-3)(t*t+1)+B(t-1)(t*t+1)+(Ct+D)(t-1)(t-3)
Substitute your A, B, C and D.
And then take t as 2, you can see that they are not equal.
If you take t as 100, they are equal.